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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
52.1.j.a \(2\) \(0.026\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
52.2.a.a \(1\) \(0.415\) \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) \(-\) \(q+2q^{5}-2q^{7}-3q^{9}-2q^{11}-q^{13}+\cdots\)
52.2.e.a \(2\) \(0.415\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(4\) \(-1\) \(q+(-3+3\zeta_{6})q^{3}+2q^{5}-\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
52.2.e.b \(2\) \(0.415\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(-6\) \(4\) \(q+(2-2\zeta_{6})q^{3}-3q^{5}+4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
52.2.f.a \(2\) \(0.415\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-6\) \(0\) \(q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots\)
52.2.f.b \(8\) \(0.415\) 8.0.18939904.2 None None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2}-\beta _{5}+\beta _{7})q^{2}+(1-2\beta _{1}+\cdots)q^{3}+\cdots\)
52.2.h.a \(2\) \(0.415\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(-3\) \(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
52.2.l.a \(4\) \(0.415\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(6\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
52.2.l.b \(16\) \(0.415\) 16.0.\(\cdots\).1 None None \(-2\) \(0\) \(-12\) \(0\) \(q-\beta _{12}q^{2}+(\beta _{3}+\beta _{12}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
52.3.b.a \(1\) \(1.417\) \(\Q\) \(\Q(\sqrt{-13}) \) None \(-2\) \(0\) \(0\) \(12\) \(q-2q^{2}+4q^{4}+12q^{7}-8q^{8}+9q^{9}+\cdots\)
52.3.b.b \(1\) \(1.417\) \(\Q\) \(\Q(\sqrt{-13}) \) None \(2\) \(0\) \(0\) \(-12\) \(q+2q^{2}+4q^{4}-12q^{7}+8q^{8}+9q^{9}+\cdots\)
52.3.b.c \(2\) \(1.417\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-4q^{4}+4iq^{5}-4iq^{8}+9q^{9}+\cdots\)
52.3.b.d \(8\) \(1.417\) 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots\)
52.3.c.a \(12\) \(1.417\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{2}q^{3}+\beta _{9}q^{4}+\beta _{8}q^{5}+\cdots\)
52.3.g.a \(6\) \(1.417\) 6.0.\(\cdots\).3 None None \(0\) \(0\) \(-6\) \(6\) \(q+\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
52.3.i.a \(4\) \(1.417\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+4\zeta_{12}^{2}q^{4}+(3-6\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
52.3.i.b \(20\) \(1.417\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-3\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{7})q^{2}+\beta _{11}q^{3}+(-1-\beta _{6}+\cdots)q^{4}+\cdots\)
52.3.j.a \(24\) \(1.417\) None None \(-1\) \(0\) \(-12\) \(0\)
52.3.k.a \(8\) \(1.417\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(6\) \(4\) \(q+(\beta _{1}-\beta _{4}+\beta _{5})q^{3}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
52.4.a.a \(1\) \(3.068\) \(\Q\) None None \(0\) \(-3\) \(-13\) \(-11\) \(-\) \(q-3q^{3}-13q^{5}-11q^{7}-18q^{9}-2q^{11}+\cdots\)
52.4.a.b \(2\) \(3.068\) \(\Q(\sqrt{217}) \) None None \(0\) \(-3\) \(23\) \(27\) \(+\) \(q+(-1-\beta )q^{3}+(11+\beta )q^{5}+(13+\beta )q^{7}+\cdots\)
52.4.d.a \(2\) \(3.068\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-8\) \(0\) \(0\) \(q-4q^{3}-2\zeta_{6}q^{5}-9\zeta_{6}q^{7}-11q^{9}+\cdots\)
52.4.d.b \(2\) \(3.068\) \(\Q(\sqrt{-433}) \) None None \(0\) \(14\) \(0\) \(0\) \(q+7q^{3}+\beta q^{5}-\beta q^{7}+22q^{9}+(42+\cdots)q^{13}+\cdots\)
52.4.e.a \(6\) \(3.068\) 6.0.6622206867.2 None None \(0\) \(0\) \(-10\) \(-16\) \(q+(-\beta _{1}-\beta _{5})q^{3}+(-2-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
52.4.f.a \(2\) \(3.068\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(18\) \(0\) \(q+(-2-2i)q^{2}+8iq^{4}+(9+9i)q^{5}+\cdots\)
52.4.f.b \(36\) \(3.068\) None None \(2\) \(0\) \(-20\) \(0\)
52.4.h.a \(8\) \(3.068\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(-36\) \(q-\beta _{5}q^{3}+(2-3\beta _{1}+\beta _{2}-\beta _{4})q^{5}+\cdots\)
52.4.l.a \(4\) \(3.068\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(-18\) \(0\) \(q+(2\zeta_{12}+2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{2}+8\zeta_{12}q^{4}+\cdots\)
52.4.l.b \(72\) \(3.068\) None None \(-8\) \(0\) \(8\) \(0\)
52.5.b.a \(1\) \(5.375\) \(\Q\) \(\Q(\sqrt{-13}) \) None \(-4\) \(0\) \(0\) \(-46\) \(q-4q^{2}+2^{4}q^{4}-46q^{7}-2^{6}q^{8}+3^{4}q^{9}+\cdots\)
52.5.b.b \(1\) \(5.375\) \(\Q\) \(\Q(\sqrt{-13}) \) None \(4\) \(0\) \(0\) \(46\) \(q+4q^{2}+2^{4}q^{4}+46q^{7}+2^{6}q^{8}+3^{4}q^{9}+\cdots\)
52.5.b.c \(24\) \(5.375\) None None \(0\) \(0\) \(0\) \(0\)
52.5.c.a \(24\) \(5.375\) None None \(6\) \(0\) \(0\) \(0\)
52.5.g.a \(8\) \(5.375\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(-12\) \(82\) \(q-\beta _{2}q^{3}+(-2-\beta _{3}+\beta _{5})q^{5}+(11+\cdots)q^{7}+\cdots\)
52.5.i.a \(52\) \(5.375\) None None \(-3\) \(0\) \(0\) \(0\)
52.5.j.a \(4\) \(5.375\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(8\) \(0\) \(28\) \(0\) \(q+(4-4\zeta_{12}^{2})q^{2}-2^{4}\zeta_{12}^{2}q^{4}+(7+\cdots)q^{5}+\cdots\)
52.5.j.b \(48\) \(5.375\) None None \(-9\) \(0\) \(-12\) \(0\)
52.5.k.a \(20\) \(5.375\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(12\) \(28\) \(q+(-\beta _{7}+\beta _{8})q^{3}+(-1-3\beta _{3}+2\beta _{5}+\cdots)q^{5}+\cdots\)
52.6.a.a \(1\) \(8.340\) \(\Q\) None None \(0\) \(-5\) \(-3\) \(53\) \(+\) \(q-5q^{3}-3q^{5}+53q^{7}-218q^{9}-702q^{11}+\cdots\)
52.6.a.b \(1\) \(8.340\) \(\Q\) None None \(0\) \(17\) \(-91\) \(-233\) \(+\) \(q+17q^{3}-91q^{5}-233q^{7}+46q^{9}+\cdots\)
52.6.a.c \(3\) \(8.340\) 3.3.203961.1 None None \(0\) \(12\) \(8\) \(138\) \(-\) \(q+(5+2\beta _{1}-\beta _{2})q^{3}+(6+5\beta _{1}-5\beta _{2})q^{5}+\cdots\)
52.6.d.a \(6\) \(8.340\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+(118+\beta _{3}+\cdots)q^{9}+\cdots\)
52.6.e.a \(12\) \(8.340\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-9\) \(-22\) \(7\) \(q+(\beta _{1}+2\beta _{2})q^{3}+(-2+\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots\)
52.6.f.a \(2\) \(8.340\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-8\) \(0\) \(-6\) \(0\) \(q+(-4-4i)q^{2}+2^{5}iq^{4}+(-3-3i)q^{5}+\cdots\)
52.6.f.b \(64\) \(8.340\) None None \(6\) \(0\) \(40\) \(0\)
52.6.h.a \(10\) \(8.340\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(9\) \(0\) \(-87\) \(q+(2\beta _{1}-\beta _{4})q^{3}+(-6+12\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
52.6.l.a \(4\) \(8.340\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(8\) \(0\) \(6\) \(0\) \(q+(4\zeta_{12}+4\zeta_{12}^{2}-4\zeta_{12}^{3})q^{2}+2^{5}\zeta_{12}q^{4}+\cdots\)
52.6.l.b \(128\) \(8.340\) None None \(-12\) \(0\) \(-52\) \(0\)
52.7.b.a \(1\) \(11.963\) \(\Q\) \(\Q(\sqrt{-13}) \) None \(-8\) \(0\) \(0\) \(-36\) \(q-8q^{2}+2^{6}q^{4}-6^{2}q^{7}-2^{9}q^{8}+3^{6}q^{9}+\cdots\)
52.7.b.b \(1\) \(11.963\) \(\Q\) \(\Q(\sqrt{-13}) \) None \(8\) \(0\) \(0\) \(36\) \(q+8q^{2}+2^{6}q^{4}+6^{2}q^{7}+2^{9}q^{8}+3^{6}q^{9}+\cdots\)
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